Sensitivity analysis of ray-tracing techniques to ionospheric electron density profiles

The Earth's ionosphere, a weakly ionized plasma embedded in a magnetic field, constitutes an anisotropic and dispersive medium for the propagation of HF radio waves. Ray-tracing is a powerful and useful technique, included in several radar simulation codes, that allows determining the path of these radio waves through the ionosphere in order, for example, to locate and track a target. Depending on the degree of precision needed, ray-tracing requires more or less precise knowledge of ionospheric conditions along the propagation path. A sensitivity analysis is performed in this work to determine the effect of different electron density height profiles in ray path features considering a fully analytical approach and two ray-tracing algorithms. The analytical approach is based on the quasi-parabolic electron density height distribution which allows for the derivation of exact equations for ray path parameters. The first ray-tracing algorithm consists of Snell-law application to a two-dimensional ionosphere which is layered into thin homogeneous slabs with a constant refractive index. The second algorithm implements the code of Jones and Stephenson, introduced in 1975, and numerically solves Haselgrove ray equations to trace ray paths through an anisotropic medium whose refractive index varies in three dimensions. The three methodologies used to assess an HF signal ray path must assume an electron density height profile which strongly affects any output parameter that depends on the signal traveling path. In particular, the analytical approach, even though it is less accurate, it is considerably faster than any numerical ray-tracing technique. This sensitivity analysis approach allows estimating the percentage variation of ray-tracing outputs which may serve to analyze the errors introduced by ionospheric transient disturbances which cannot be easily included in models considered in ray-tracing algorithms.